Detecting and diagnosing faults without a priori knowledge are important requirements in monitoring practical industrial processes. Principal component analysis (PCA) and multivariate contribution analysis (MCA) methods belong to this category of unsupervised monitoring methods. Because the processes' operation conditions and parameters may vary with time, there is a need to online update the monitoring statistics. This paper presents an adaptive approach for fault detection and diagnosis depending on an orthogonal iteration method, i.e., the fast data projection method (FDPM), which is known as the lowest complexity one among all known subspace tracking methods. The faults are first detected using four adaptive indices of PCA, i.e., Hotelling's T-2, Hawkins' T-H(2), SPE, and a combined index psi. Second, adaptive diagnosis methods based on multivariate contribution analysis (MCA) are used to diagnose faults in time-varying processes. The diagnosability of the adaptive diagnosis methods is investigated, and a comparison of the adaptive diagnosis methods for the four indices is conducted. The effectiveness of the adaptive PCA- and MCA-based diagnosis methods is demonstrated by three simulation studies: a numerical example, the continuous stirred-tank reactor (CSTR) chemical process, and the Tennessee Eastman process.